Distributed Variational Inference-Based Heteroscedastic Gaussian Process Metamodeling

In this paper, we generalize the variational Bayesian inference-based Gaussian process (VBGP) modeling approach for handling large-scale heteroscedastic datasets. VBGP is suitable for simultaneously estimating the underlying mean and variance functions with a single simulation output available at each design point. To improve the scalability of VBGP, we consider building distributed VBGP (DVBGP) models and their hierarchical versions by partitioning a dataset and aggregating individual subset VBGP predictions based on the idea of "transductive combination of GP experts." Numerical evaluations are performed to demonstrate the performance of the DVBGP models from which some insights are derived.